cleaning with kerosene and supplies

Thanks for the info! The wicker we have is very dark brown, almost mahogany. Some of the wicker that has come off has a wire down the middle. It came with a cottage my grandparents purchased from the original owners that was built in 1929, so we assume it was purchased shortly after the cottage was built. I think from reading other websites it may be the paper type that is wound but I'm not sure, should we clean with kerosene if it's this type? Also do you know if there are any supply companies that sell this type of wicker? Thanks for any info!